Apart from being drafted, how would a person enlist to fight during WW2?

"Voluntary induction" if the man was subject to Selective Service, or voluntary enlistment if he was outside the bounds of Selective Service as stipulated by the executive order (i.e., being younger than eighteen or older than thirty-seven). Men younger than eighteen were not allowed to be subject to active duty until after their eighteenth birthdays if they enlisted in the Army due to legislative restriction. The Navy had no such legislative restriction on the enlistment of men aged seventeen, who could enter basic training and be assigned to active duty immediately, and made options about service more well-known to this age group than the Army. The vast majority of militarily-eligible seventeen year olds thus chose to voluntarily enlist in the Navy, much to the chagrin of the Army, who desired their proportion of this quality manpower, especially for the ground forces.

Men older than thirty-seven were still liable for induction by law, but were deemed unacceptable to any of the armed services after the date specified in the executive order, except in a few instances such as certain specialist civilian jobs desirable to the armed forces like doctors. A much smaller number of older men to begin with could meet the physical and psychological requirements for service.

Men who had expressed a willingness to voluntarily induct themselves and had filled out the proper paperwork were to be selected first when a local board filled its call, ahead of what could be considered "normal" draftees. The overall Selective Service procedure for "voluntary induction" being:

The end of voluntary enlistments, however, did not mean the end of voluntary inductions. This procedure for entering the armed forces, as already described, continued....Although no longer permitted to enlist, men could still volunteer for induction, prior to receiving an order to report for induction, by filing an Application for Voluntary Induction (DSS Form 165) with their local boards. A registrant filing such an application had the right to express his preference as to branch of service. His assignment, after induction, depended upon his qualifications and the requirements of that service. Upon filing an application for voluntary induction with a local board, a volunteer who was not a registrant was registered and then processed in the same manner as all other registrants. On his Registration Card (DSS Form 1), the letter “V” was written-in the place marked "Order No." to indicate that he had volunteered. If he was not deferrable under the act or the regulations, he was then placed in Class I-A, available for service. As a volunteer he was the first to be ordered to report for induction by his local board in filling a call.

If voluntarily inducting himself, a man could express a preference of which service he wished to be assigned to (“Army” or “Navy;” the latter included the Marine Corps and Coast Guard), but he was subject to assignment to either service depending upon age, physical and psychological, occupational, and educational qualities, the present needs of the service, and whether the quota for that service had been filled at the particular time. The Marine Corps maintained a special arrangement with the Selective Service System after the end of voluntary enlistment in order to obtain willing personnel whereby a man could be released from the custody of Selective Service and “voluntarily enlist” as a Marine:

At this point, the Marine Corps liaison officers entered the picture. Through their influence with state and local selective service officials, they were able to postpone the induction of draftees who wanted to serve with the Marine Corps until a vacancy in the quota occurred. Through this process, the Marine Corps was able to procure individuals of high caliber who were anxious to serve in its ranks.

The induction and processing of Marine inductees were the duties of the Recruiting Service and were performed as they had been for volunteers. At first, all inductees were enrolled as Selective Service, but after 25 February 1943 the Recruiting Service was authorized to discharge inductees to permit then to enlist in the regular or Reserve Marine Corps. As some stigma came to be attached to selective service inductees, unjustified of course, this pseudo-voluntary procedure became very popular. Of a total of 224,323 inductees, fewer than 70,000 chose to remain in inductee status.

The sequence of induction under Selective Service being:

Period	Sequence
November 1940-15 July 1942	(1) Volunteers in the sequence of their volunteering; (2) Other registrants in the sequence of their order numbers.
15 July 1942-12 April 1943	(1) Volunteers; (2) Registrants without dependents; (3) Registrants with collateral dependents or with wives and children with whom they do not maintain a bona fide family relationship in their homes; (4) Registrants with wives (but no children); (5) Registrants with wives and children, or children with whom they maintain a bona fide family relationship in their homes.
12-27 April 1943	(1a) Volunteers; (1) Single men with no dependents; (2) Single men with collateral dependents; (3) Married men with wives only; (4) Men with children.
27 April-31 July 1943	(1a) Volunteers; (1) Men with no dependents. All men not qualified for group 2, group 3, or group 4 below, were for this purpose to be considered as men with no dependents; (2) Men with collateral dependents, provided such status was acquired prior to December 8, 1941; (3) Men who had wives with whom they maintained a bona fide family relationship in their homes, provided such status was acquired prior to December 8, 1941; (4) Men who had children with whom they maintained a bona fide family relationship in their homes, provided such status was acquired prior to December 8, 1941.
31 July-10 December 1943	(1a) Volunteers; (1) Men with no dependents. All men not qualified for group 2, group 3, or group 4 below were for this purpose, to be considered as men with no dependents; (2) Men with collateral dependents, provided such status was acquired prior to December 8, 1941; (3) Men who had wives with whom they maintained a bona fide family relationship in their homes, provided such status was acquired prior to December 8, 1941; (4) Men who had children with whom they maintained a bona fide family relationship in their homes, provided such status was acquired prior to December 8, 1941.^3 A registrant placed in Class I-A or Class I-A-O because he left an agricultural occupation or an agricultural endeavor (see sec. 622.31-2) or because he was engaged in a nondeferrable activity or occupation (Local Board Memorandum No. 181) was to be inducted prior to those men reclassified from Class III-A into Class I-A or Class I-A-O pursuant to this memorandum.

(3) A child born on or before September 14, 1942, was to be considered as having been conceived prior to December 8, 1941, and a child born on or after September 15, 1942, was to be considered as having been conceived on or after December 8, 1941, unless there was affirmative evidence of a medical character which clearly established that birth was delayed.

As men with children became liable to be drafted on 1 October 1943, Public Law 197 was passed on 10 December 1943 to ensure that men classified as "fathers" (i.e., married men with children conceived prior to 8 December 1941) would be inducted only after all "nonfathers" had been taken.

Period	Sequence
10 December 1943-10 January 1944	(1) Volunteers; (2) Fathers; (3) Nonfathers

A father was defined as a registrant who was married prior to December 8, 1941, who had maintained a bona fide family relationship with his family since that date and who had a child as defined in section 622.33 (a), Selective Service Regulations....